In AT-cut quartz crystal resonating elements, the vibration mode of a primary vibration to be excited is the thickness-shear vibration. The AT-cut quartz crystal resonating elements are suitable for downsizing and higher frequency and exhibit an excellent cubic curve in frequency-temperature characteristics, and therefore have been used in many areas such as piezoelectric oscillators and electronic apparatuses.
The AT-cut quartz crystal resonating element includes an AT-cut quartz crystal substrate and a pair of excitation electrodes provided on both surfaces of the AT-cut quartz crystal substrate. By applying an alternating voltage between the pair of excitation electrodes, the primary vibration (thickness-shear vibration) is excited. Here, in an AT-cut quartz crystal resonator of JP-A-4-276915, for suppressing a secondary vibration (spurious) other than the primary vibration, the shape of each of excitation electrodes is a “constricted” shape in which the width of a central portion in an X-axis direction is made narrower than the width of both ends. Although the spurious may be suppressed to some extent even with such a configuration, the effect is not sufficient.
The reason will be described below. In the AT-cut quartz crystal resonator of JP-A-4-276915, a flat plate-like AT-cut quartz crystal substrate with a constant thickness is used. In such an AT-cut quartz crystal substrate, a region interposed between a pair of excitation electrodes is a vibration region, and within the vibration region, a vibration region of the primary vibration and a vibration region of the secondary vibration are generated. In other words, even when the occurrence of the spurious is attempted to be suppressed through the contrivance of the shape of the excitation electrode as in JP-A-4-276915, the vibration region of the secondary vibration is inevitably generated in the vibration region, which causes the excitation of the secondary vibration.